Question

A car initially at rest starts with a uniform acceleration and gains a velocity of 20m/s in 4s.The displacement of the car is

Answer 1

by formula
$v = u + at \\ \\ 20 = 0 + a \times 4 \\ \\ 20 = 4a \\ \\ a = \frac{20}{4} \\ \\ a = 5$
so acceleration comes 5 m/s^2

again by other formula

$s = ut + a {t}^{2} \\ \\ s = 0 + 5 \times {4 }^{2} \\ \\ s = 5 \times 16 \\ \\ s = 80$
so distance comes = 80 m

Answer 2

✬ Displacement = 40 m ✬

Explanation:

Given:

• A car starts from rest (u) = 0 m/s.
• Car gains velocity (v) of 20 m/s.
• Time taken by car to attain final velocity = 4 seconds.

To Find:

• What is the displacement of car ?

Formula to be used:

• v = u + at ( For acceleration )
• s = ut + 1/2at² ( For displacement )

Solution: Putting the values on first formula

$\implies{\rm }$ v = u + at

$\implies{\rm }$ 20 = 0 + a $\times$ 4

$\implies{\rm }$ 20 = 0 + 4a

$\implies{\rm }$ 20 = 4a

$\implies{\rm }$ 20/4 = a

$\implies{\rm }$ 5 m/s² = a

So, The acceleration of car is 5 m/s².

Now, For displacement use the second formula

$\implies{\rm }$ s = ut + 1/2at²

$\implies{\rm }$ s = 0 $\times$ 4 + 1/2 $\times$ 5 $\times$ 4²

$\implies{\rm }$ s = 0 + 5/2 $\times$ 16

$\implies{\rm }$ s = 5 $\times$ 8

$\implies{\rm }$ s = 40 m

Hence, the displacement of the car is 40 m.