Question

a car accelerates with a constant acceleration of 1.2ms^-1 along a long straight road.how long does it take the car to accelerate from 100kph to 110kph,and how far does it travel while doing so?

Answer 1

Given:-

Acceleration(a) =1.2 m/s²

Car speed(accelerate from).

$u=100 kph = 72.78 m/s.\\[5pt] v = 110 kph = 30.56 m/s.$

Now,

From Kinetic equation.

$v=u+at\\[5pt] \\t=\frac{v-u}{a}\\[8pt] \\t=\frac{30..56 m/s-27.78 m/s}{1.2 m/s^{2}}\\[5pt] t=2.315 sec.$

So,

The time taken by car to travel from speed .

$\\t=2.315 sec.$

Now,

Again , use following kinetic equation .

$v^{2}-u^{2}=2as\\[5pt] s=\frac{v^{2}-u^{2}}{2a}\\[5pt] s=\frac{(30.56m/s)^{2}-(27.78m/s)^{2}}{2\times 1.2m/s^{2}}\\[5pt] s=67.56 m$

So,

The distance traveled by the the car is.

$s=67.56 m$