Question

If the car passes point A with a speed of 20m/s and begins to increase its speed at a constant rate of At=0.5m/s^2, determine the magnitude of the car's acceleration when s=100m and x=0.

Answer 1

Using the equation for displacement with initial velocity, the magnitude of the car's acceleration when s=100m and x=0 is 10m/s^2.

Step-by-step explanation:

To determine the magnitude of the car's acceleration when s = 100m and x = 0, we can use the equation for displacement with initial velocity (V0 = 20m/s) and constant acceleration (A = 0.5m/s^2):

x = xo + V0t + 1/2At^2

Since the car starts from rest (x0 = 0), the equation simplifies to:

x = 1/2At^2

Plugging in the values for s, x, V0, and solving for A:

100 = 1/2(0.5)t^2

t^2 = 400

t = 20s

Now, we can plug the value of t into the equation for acceleration:

A = 0.5(20) = 10m/s^2