Physicssssss HWK????????????
At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 1.8 m/s2. At the same instant a truck is 10.2 m down the road and traveling with a constant speed of 8.5 m/s. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the automobile be traveling at that instant?
More Questions From This User See All
Answers & Comments
Verified answer
Write equations that express each vehicle's position ("x") as a function of time:
Car:
x_car = ½at² + (v_initial)t + x_initial
But v_initial and x_initial are zero for the car: so:
x_car = ½at² = ½(1.8m/s²)t²
Truck:
x_truck = ½at² + (v_initial)t + x_initial
For the truck: a=0, v_initial=8.5m/s, x_initial=10.2m. So:
x_truck = (8.5m/s)t + 10.2m
At some time "t_overtake", the car will overtake the truck, which means x_car and x_truck will be the same at that instant:
At t = t_overtake:
x_car = x_truck
which means:
½(1.8m/s²)(t_overtake)² = (8.5m/s)(t_overtake) + 10.2m
Solve for "t_overtake", and that answers part (a).
For part(b), write the car's speed as a function of time:
v_car = at = (1.8m/s²)t
That means at the time of overtaking,
v_car = (1.8m/s²)(t_overtake)
Plug in the value of "t_overtake" that you calculated above.