## Question

The displacement *y* (in metres) of a body varies with time *t* (in seconds) as

How long does the body take to come to rest?

### Solution

12 seconds

Given,

.

Comparing it with

,

We have,

.

For a body to come to rest, the final velocity *v* = 0. Using these values of*u*, *v* and *a* in relation

We have

.

#### SIMILAR QUESTIONS

A cyclist starts from the centre *O* of a circular track of radius *r* = 1 km, reaches the edge *P* of the track and then cycles along circumference and stops at point *Q*. if the total time take is 10 min, what is the average velocity of the cyclist?

Give the speed-time graph of the motion of a car. What is the ratio of the distance travelled by the during the last two seconds to the total distance travelled in seven seconds?

A stone falls from rest. The distance covered by the stone in the last second of its motion equals the distance covered by it during the first three seconds of its motion. How long does the stone take to reach the ground?

Two balls of masses *m*_{1} and *m*_{2} are thrown vertically upward with the speed *u*. If air resistance is neglected, they will pass through their point of projection in the downward direction with a speed

A train covers half of its journey with a speed of 20 ms^{–1} and the other half with a speed of 30 ms^{–1}. The average speed of the train during the whole journey is

A body goes from *A* to *B* with a velocity of 40 kmh^{–1} and returns from *B*to *A* with a velocity of 60 kmh^{–1}. What is the average velocity of the body during the whole journey?

The area under the velocity-time graph between any two instants *t* = *t*_{1}and *t* = *t*_{2} gives the distance covered in time

A particle is given a displacement of 4 m in the *x*-*y* plane. If the *x*-component of the displacement vector is 2 m, the y-component will be

A car, starting from rest, accelerates at a constant rate of 5 ms^{–2} for some time. It then retards at a constant rate of 10 ms^{–2} and finally comes to rest. If the total taken is 6 *s*, What is the maximum speed attained by the car?

A body, starting from rest, moves in a straight line with a constant acceleration *a* for a time interval *t* during which it travels a distance *s*_{1}. If continues to move with the same acceleration for the next time interval *t*during which it travels a distance *s*_{2}. The relation between *s*_{1} and *s*_{2} is