Physics problem - Do i have this right?

Question

"A car is traveling at 45m/s and passes a truck. Two seconds later and with acceleration (2 m/s^2) the truck starts after the car. How long in seconds does it take to catch the car?"

I think it might be 32.7 seconds. Am I right?

Answer 1

I guess that the truck was starting from rest?

The car will have displacement
x(t)=45*t
the truck will have
x(t)=.5*2*(t-2)^2 for t>=2

find when the x(t)'s are equal

45*t=t^2-4*t+4
make a standard quadratic
t^2-49*t+4=0

I get that t=49 seconds, which is after the car passed. Or 47 seconds after the truck started.

j

Answer 2

Dc = 90 + 45t
Dt = ½*2*t²
Dc = Dt→ t²- 45t - 90 = 0 → t = 46.92 sec

......If I solved the quadratic right!