Acar is stationary in front of a red stop light. as the light turns green, a truck goes past at a constant speed of 15 m/s. at the same moment the car begins to accelerate at 1.25 m/s2 ; when it reaches 25 m/s, the car continues at that speed. when (time) will the car pass the truck?

The car will pass the truck 25 s after leaving the traffic light

Explanation:

These equations apply for a straight movement with constant acceleration:

x = x0 + v0 t + 1/2 a t²

v = v0 + a t

where:

x = position at time t

x0 = initial position

a = acceleration

v0 = initial speed

v = speed

t = time

For a straight movement with constant speed, as the truck:

x = x0 + v t

First, let´s calculate how much time the car accelerates, using the equation of speed:

v = v0 + a t

25 m/s = 0 m/s + 1.25 m/s² * t

t = 25 m/s / 1.25 m/s²

t = 20 s

Now, let´s see the position of the car and the truck at that time:

The position of the car will be:

x = x0 + v0 t + 1/2 a t²

since it starts from rest and considering the the traffic light the initial point:

v0 = 0

x0 = 0

then

x = 1/2 *1.25 m/s² * (20 s)² = 250 m

The truck position at that time will be:

x = x0 + v * t = 15 m/s * 20 s = 300 m (considering the traffic light as the initial position)

Then, the truck is 50 m ahead of the car when the car reaches it´s maximum speed.

Now, we have to find the time at which the car and the truck have the same position.

For the car, the equation for the position is:

x = x0 + v t

Now, let´s consider x0 as the position at which the car starts traveling at constant speed, that is, 250 m.

For the truck, the equation of the position will also be:

x = x0 + v t

And now x0 will be the position at t = 20 s, when the car starts traveling at  constant speed, that is, 300 m. So, we have a chase in which the truck starts at the same time that the car but 50 m ahead of it traveling at 15 m/s while the car travels at 25 m/s.

Since the position of the car and the truck will be the same when the car passes the truck:

x car = x truck

x0 car + v car * t = x0 truck + v truck * t

250 m + 25 m/s * t = 300 m + 15 m/s * t

25 m/s * t  - 15 m/s * t = 300 m - 250 m

10 m/s * t = 50 m

t = 50 m / 10 m/s = 5 s

After 25 s, the car will pass the truck.

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