# Motion in a Straight Line Class 11 Problems with Solutions - Subjective

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## Motion in a Straight Line Class 11 Problems with Solutions

**Q. Can a body be said to be at rest as well as in motion at the same time.**

**Q. Can a body have zero velocity but yet possesses acceleration?**

**Q. Under what condition will the distance and displacement of a moving object will have the same magnitude?**

**Q. What does speedometer of a car indicate?**

**Q. As the body moves in a straight line, it moves smaller and smaller distances in equal intervals of time.**

**Q. Derive an expression for stopping distance of a vehicle in terms of initial velocity and deceleration a.**[NCERT]

**Q. Explain clearly, with examples, the distinction between : (a) magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval; (b) magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first. When is the quality sign true?**[NCERT]

**Q. Derive three equations of motion by calculus method. Express conditions under which they can be used.**

**Q. Can a body have constant velocity and still have varying speed?**

**Q. Are rest and motion absolute or relative terms?**

**Q. Why the speed of the object can never be negative?**

**Q. Define instantaneous velocity.**Sol. Velocity of a body at a particular instant is called Instantaneous velocity. $\mathrm{v}=\frac{\mathrm{dx}}{\mathrm{dt}}$ and $\operatorname{Lt}_{\mathrm{st} \rightarrow 0}\left(\frac{\mathrm{dx}}{\mathrm{dt}}\right)$

**Q. What is average velocity?**

**Q. The position of an object moving along -axis is given by where and is measured in second. What is it velocity at and . What is the average velocity between and**[NCERT]

**Q. A jet air plane travelling at the speed of ejects its products of combustion at the speed to relative to the jet plane. What is the speed of the combustion products w.r.t. an observer on the ground?**[NCERT]

**Speed of combustion product w.r.t. observer on the ground $=?$ Velocity of jet air plane w.r.t. observer on ground $=500 \mathrm{kmh}^{-1}$ If $\overrightarrow{\mathrm{v}}_{\mathrm{j}}$ and $\overrightarrow{\mathrm{v}}_{\mathrm{o}}$ represent the velocities of jet and observer respectively, then $\mathrm{v}_{\mathrm{j}}-\mathrm{v}_{\mathrm{o}}=500 \mathrm{kmh}^{-1}$**Similarly, If $\vec{v}_{\mathrm{c}}$ represents the velocity of the combustion products $w \cdot r .$ jet plane, then, $\mathrm{v}_{\mathrm{c}}-\mathrm{v}_{\mathrm{j}}=-1500 \mathrm{kmh}^{-1}$ The negative sign indicates that the combustion products move in a direction opposite to that of jet. Speed of combustion products w.r.t. observer $=v_{c}-v_{o}=\left(v_{c}-v_{j}\right)+\left(v_{j}-v_{o}\right)$ $=(-1500+500) \mathrm{kmh}^{-1}=-1000 \mathrm{kmh}^{-1}$

**Q. A police van moving on a highway with a speed of fires a bullet at a thief's car speeding away in the same direction with a speed of . If the muzzle speed of the bullet is , with what speed does the bullet hit the thief's car?**[NCERT]

**Q. Four persons K, L, M and start from the vertices of a square of side , simultaneously and move towards the neighbour in order always with the same speed of . When and where do they meet.**[NCERT]

**As $K, L, M$ and $N$ move towards the next person in order after a short time they will be at $K^{\prime}, L^{\prime}$ $M^{\prime}$ and $N^{\prime}$ respectively. The size to the square reduces. It indicates that they have come closer. After next short interval if they are at $K^{\prime \prime}, L^{\prime \prime}$ $M^{\prime \prime}$ and $N^{\prime \prime},$ the size of the square further reduces.**Finally, they will follow a curvi-linear path and meet at $O,$ the centre of the square. We know, the time taken $=\frac{\text { displacement }}{\text { Velocity in the direction of displacement }}$ Β $\therefore \quad \mathrm{t}=\frac{\mathrm{LO}}{\left(\frac{\mathrm{v}}{\sqrt{2}}\right)}=\frac{\frac{\mathrm{a}}{\sqrt{2}}}{\frac{\mathrm{v}}{\sqrt{2}}}=\frac{\mathrm{a}}{\mathrm{v}}$

**Q. On a two-lane road, car is travelling with a speed of . Two cars and approach car in opposite directions with a speed of each. At a certain instant, when distance. A B is equal to A C, both being decides to overtake before does. What minimum acceleration of is required to avoid**

**an accident?**[NCERT]

**Q. On a long horizontal moving belt, a child runs to and fro with a speed (with respect to the belt between his father and mother located apart on the moving belt. The belt moves with . speed of For an observer on a stationary . platform outside, what is the :**

**(a) speed of the belt child running in the direction of motion of the belt ?**

**(b) speed of the child running opposite to the direction of motion of the belt?**

**(c) time taken by**

**child in (a) and (b)? Which of the answer alter if motion is viewed by one of the parents?**[NCERT]

**Q. A man walks on a straight road from his home to**

**a market away with a speed of F**

**inding the market closed, he instantly turns and**

**walks back home with a speed of .**

**What is the**

**(a) magnitude of average velocity, and (b) average**

**speed of the man over the following intervals of**

**time : (i) 0 to 30 min (ii) 0 to 50 min (iii) 0 to**

**40 min?**[NCERT]

**Q. A boy standing on a stationary lift (open from**

**above) throws a ball upwards with the maximum**

**initial speed he can, equal to . (a) How**

**much time does the ball take to return to his hands**

**b) If the lift starts moving up with a uniform**

**speed of , and the boy again throws the**

**ball up with the maximum speed he can, how long**

**does the ball take to return to his hands?**

**Q. A woman starts from her home at $9.00 A M,$ walks**

**with a speed pf on a straight road up to**

**her office away, stays at the office up to**

**and returns home by an auto with a speed**

**of . Choose suitable scales and plot the**

**graph of the motion.**[NCERT]

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