Question

a car starts from rest and attains a speed of 4m/s in 8s

a . calculate the acceleration of the car

b . calculate the distance it has covered during this time

c . what velocity would it attain at the end of 10s

Answer 1

a) We can calculate the acceleration of the car from the kinematic equation:

$$v=v_0+at,$$ $$a=\dfrac{v-v_0}{t}=\dfrac{4\ \dfrac{m}{s}-0\ \dfrac{m}{s}}{8\ s}=0.5\ \dfrac{m}{s^2}.$$

b) We can calculate the distance that the car has covered during this time from the another kinematic equation:

$$d=v_0t+\dfrac{1}{2}at^2,$$ $$d=0\ \dfrac{m}{s}\cdot 8\ s+\dfrac{1}{2}\cdot 0.5\ \dfrac{m}{s^2}\cdot (8\ s)^2=16\ m.$$

c) We can calculate the the velocity that the car would attain at the end of 10 s from

the kinematic equation:

$$v=v_0+at,$$ $$v(10\ s)=0\ \dfrac{m}{s}+0.5\ \dfrac{m}{s^2}\cdot 10\ s=5\ \dfrac{m}{s}.$$

Answer:

a) $a=0.5\ \dfrac{m}{s^2}.$

b) $d=16\ m.$

c) $v(10\ s)=5\ \dfrac{m}{s}.$