# NCERT Class 11 Physics Solutions: Chapter 3 – Motion in a Straight Line Part 6 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question: 3.11**

Read each statement below carefully and state with reasons and examples, if it is true or false;

A particle in one-dimensional motion

a) With zero speed at an instant may have non-zero acceleration at that instant

b) With zero speed may have non-zero velocity

c) With constant speed must have zero acceleration

d) With positive value of acceleration must be speeding up.

**Answer**:

A)

- True
- When an object is thrown vertically up in the air, its speed becomes zero at maximum height. However, it has acceleration equal to the acceleration due to gravity (g) that acts in the downward direction at that point.

b)

- False
- Speed is the magnitude of velocity. When speed is zero, the magnitude of velocity along with the velocity is zero.

c)

- True
- A car moving on a straight highway with constant speed will have constant velocity. Since acceleration is defined as the rate of change of velocity, acceleration of the car is also zero.

d)

- False
- This statement is false in the situation when acceleration is positive and velocity is negative at the instant time taken as origin. Then, for all the time before velocity becomes zero, there is slowing down of the particle. Such a case happens when a particle is projected upwards.
- This statement is true when both velocity and acceleration are positive, at the instant time taken as origin. Such a case happens when a particle is moving with positive acceleration or falling vertically downwards from a height.

**Question 3.12**:

A ball is dropped from a height of 90 m on a floor. At each collision with the floor, the ball loses one tenth of its speed. Plot the speed-time graph of its motion between

**Answer**:

- Ball is dropped from a height,
- Initial velocity of the ball,
- Acceleration,
- Final velocity of the ball
- From second equation of motion, time (t) taken by the ball to hit the ground can be obtained as:

- From first equation of motion, final velocity is given as:

- Rebound velocity of the ball,
- Time (t) taken by the ball to reach maximum height is obtained with the help of first equation of motion as:

- Total time taken by the ball

- As the time of ascent is equal to the time of descent, the ball taken 3.86 s to strike back on the floor for the second time.
- The velocity with which the ball rebounds from the floor

- Total time taken by the ball for second rebound

- The speed – time graph of the ball is represented in the given figure as: