Answer to Question #22849 in Mechanics | Relativity for jmtrasfiero

Question

A car and a truck start from rest at the same instant with the car initially at same distance behind the truck. The truck has constant acceleration of 3.4 m/s^2. The car overtakes the truck within the truck has moved a distance of 40.0 m.

a. How far was the car behind the truck initially?
b. How much time does it take the car to overtake the truck?
c. What are their speeds when they are abreast?

Answer 1

If the car has constant acceleration of a m/s^2:
s=a*t^2/2
s - distance
t - time
b. for truck:
s = a_t*t^2/2
a_t - the truck acceleration
t = Sqrt[2s/a_t] = Sqrt[2*40/3.4] = 4.85 sec
a. for car:
s_c = a*t^2/2
s_c = a/a_t*s = a/3.4*40 = a*11.8 m
the car behind the truck initially:
d = s_c - s = a/3.4*40 - 40 = (a/3.4 - 1)*40 m
c. v = a*t
v - speed
a - acceleration
t - time
for truck:
v = a_t*t = a_t*Sqrt[2s/a_t] = Sqrt[2s*a_t]=Sqrt[2*40*3.4] = 16.5 m/s
for car:
v = a*t = a*Sqrt[2s/a] = Sqrt[2s*a]