Answer to Question #198764 in Mechanics | Relativity for Master j

Question

A test driver accelerates a car uniformly at a rate of 2m/s² starting from rest to a velocity of 24m/s. The car maintains this velocity for T seconds and then retards uniformly to a velocity of 16m/s in a further 10 seconds.

(i) sketch a velocity-time diagram of the motion of the car

Find(ii) the time elapsed during the acceleration

(iii) the distance travelled during the acceleration,

(iv) the distance travelled during 10 seconds retardation,

(v) the value of T, given that the total distance travelled by that car is 1496 meters

Answer 1

Solution.

$v_0=0;$

$a=2 m/s^2;$

$v_1=24m/s;$

$t_2=10s;$

$i)$

$ii) a=\dfrac{v-v_0}{t}\implies t_1=\dfrac{v-v_0}{a}= \dfrac{24-0}{2}=12s;$

$iii) S_1=\dfrac{v_1^2-v_0^2}{2a}= \dfrac{24^2-0^2}{2\sdot2}=144m;$

$iv)S_2=\dfrac{v_1+v_2}{2}\sdot t=\dfrac{24+16}{2}\sdot10=200m;$

$v)S=1496-(S_1+S_2)=1496-344=1152m;$

$T=\dfrac{S}{v_1}=\dfrac{1152}{24}=48s;$

Answer: $ii)12s;$

$iii)144m;$

$iv)200m;$

$v)48s.$