Question

the acceleration of a car is 2m/s^2 and another car has constant velocity of 35m/s.what time the first car overtake the car with constant velocity of the first car?

draw and show solution

Answer 1

first car:
a = 2 m/s^2
v = 2t + c
when t = 0 , v = 0 m/s
0 = 0 + c , so c=0
so v = 2t
d = t^2 + k
when t = 0, d = 0
0 = 0 + k, so k=0

for 1st car: d = t^2

2nd car:
v = 35
d = 35t + c
when t= 0 , d = 0 , so c = 0

for 2nd car : d = 35t

so we want t^2 = 35t
t^2 - 35t = 0
t(t-35) = 0
t = 0 , (at the start they both had traveled no distance)
or
t = 35

the 1st car will catch the second car in 35 seconds