Question

1. if a child on a bicycle can accelerate at an average rate of 0.53 m/s², how long would it take to increase the bicycles velocity from 0.68 m/s n to 0.89 m/s n?
2. (a) while approaching a red light, a student driver begins to apply the brakes. if the cars brakes can cause an average acceleration of 2.90 m/s² s and it takes 5.72 s for the car to come to rest, what was the cars initial velocity?

(b) what is the significance of the direction of the initial velocity and that of the acceleration?

Explanation:

Problem 8

Discipline and Subfield

Natural Science - Physics

Step - by - Step Format

Step 1: Use the kinematic equation \(v = v_0+at\)

We want to find \(t\), and we can rewrite the equation as \(t=\frac{v - v_0}{a}\). Here, \(v_0 = 0.68\ m/s\), \(v = 0.89\ m/s\), and \(a=0.53\ m/s^{2}\)

Step 2: Substitute the values into the formula

\(t=\frac{0.89 - 0.68}{0.53}\)
\(t=\frac{0.21}{0.53}\approx0.396\ s\)

Step 1: Use the kinematic equation \(v = v_0+at\)

We know that \(v = 0\) (comes to rest), \(a=- 2.90\ m/s^{2}\) (de - acceleration), and \(t = 5.72\ s\). Rearranging the equation for \(v_0\) gives \(v_0=v - at\)

Step 2: Substitute the values into the formula

\(v_0=0-(-2.90)\times5.72\)
\(v_0 = 2.90\times5.72\)
\(v_0=16.588\ m/s\approx16.6\ m/s\)

The negative sign of acceleration indicates that the acceleration is in the opposite direction of the initial velocity. Since the car is coming to rest (decelerating), the force applied by the brakes (which causes the acceleration) is opposite to the direction of motion (initial velocity).

Answer:

\(t\approx0.40\ s\)

Problem 9(a)

Discipline and Subfield

Natural Science - Physics

Step - by - Step Format