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

Answer:

$d=1600\ m$

Explanation:

Let d be the displacement of the car.

Given:

$Displacement=100\ meter$

The displacement formula of an object is.

$d=v_{1} t+\frac{1}{2} a(t)^{2}$

Where $v_{1} = initial\ velocity$

$t=time$

$a=acceleration$

If the car start from rest then $v_{1} = 0$

$d=0+\frac{1}{2} a(t)^{2}$

$d=\frac{1}{2} a(t)^{2}$

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

Now substitute $t=4t$ in above equation

$d=\frac{1}{2} a(4t)^{2}$

$d=16\frac{1}{2} a(t)^{2}$

So the displacement will be 16 times more = $16\times displacement$

$d = 16\times 100$

$d = 1600\ meter$

Therefore, the displacement is $1600\ meter$.