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.

______ m

Answer 1

`d=1600\ m`

Step-by-step explanation:

Let d be the displacement of the car.

Given:

`Displacement=100\ meter`

The displacement formula of an object is.

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

Where
`v_(1) = initial\ velocity`

`t=time`

`a=acceleration`

If the car start from rest then
`v_(1) = 0`

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

`d=(1)/(2) a(t)^(2)`

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

Now substitute
`t=4t` in above equation

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

`d=16(1)/(2) a(t)^(2)`

So the displacement will be 16 times more =
`16* displacement`

`d = 16* 100`

`d = 1600\ meter`

Therefore, the displacement is
`1600\ meter`.