Question

a car starts at rest and accelerates at a rate of 2.75 m/s/s. What is its speed 3.726 seconds after it starts to move?

Answer 1

Answer: The speed is 10.2465m/s

Step-by-step explanation:

We know that a car starts to accelerate with an acceleration of 2.75m/s^2

Now, as we know, acceleration is the rate of change of the velocity, so if we want to find the speed (that is the magnitude of the velocity) we need to integrate the acceleration over time.

v(t) = 2.75m/s^2*t + c

where c is a constant of integration, and we know that the car starts at rest, so the initial velocity is equal to zero, wich means that c = 0.

v(t) = 2.75m/s^2*t

Now, we want to find the speed at t = 3.726 s

this is:

v( 3.726 s) = (2.75*3.726)m/s = 10.2465m/s

Answer 2

If the rate of acceleration is constant, than the object's velocity at a given time will be the rate of acceleration multiplied by the duration of time over which it is accelerating. In this instance, the car is accelerating at 2.75 m/s^2 for 3.726 seconds. So, multiplying 2.75*3.726, we get a speed of 10.25 m/s after this period of time.