Question

A car undergoing uniform acceleration travels 100 meters from a standing start in a given period of time. If the time were increased by a factor of four, calculate the displacement.

Answer 1

1600 m

Step-by-step explanation:

if the time factor is tripled, the displacement is nine times greater

3:9 or in this case 4:16 (because the ratio is a square)

The time is increased by a factor of 4 so,

4^2=16

16*100 = 1600

Answer 2

d = 1600 m

Step-by-step explanation:

If car start from rest and accelerates uniformly then the displacement of the car is given as

`d = v_i t + (1)/(2)at^2`

now we know

`d = 0 + (1)/(2)at^2`

now if the same car will accelerate from rest for four times of the previous time interval

then we will have

`d = 0 + (1)/(2)a(4t)^2`

`d = 16((1)/(2)at^2)`

so the distance will be 16 times more

`d = 1600 m`