Question

select the correct answer. a motorcyclist changes the velocity of his bike from 20.0 meters/second to 35.0 meters/second under a constant acceleration of 4.00 meters/second². how long does it take the bike to reach the final velocity? a. 2.02 seconds b. -2.02 seconds c. 3.75 seconds d. -3.75 seconds

Explanation:

Step1: Recall the kinematic equation

The kinematic equation relating final velocity ($v$), initial velocity ($u$), acceleration ($a$), and time ($t$) is $v = u + at$. We need to solve for $t$.

Step2: Rearrange the equation for $t$

Rearranging the equation $v = u + at$ to solve for $t$ gives $t=\frac{v - u}{a}$.

Step3: Substitute the given values

We are given $u = 20.0\space m/s$, $v = 35.0\space m/s$, and $a = 4.00\space m/s^{2}$. Substituting these values into the formula for $t$:
$t=\frac{35.0 - 20.0}{4.00}$

Step4: Calculate the value of $t$

First, calculate the numerator: $35.0 - 20.0 = 15.0$. Then divide by the denominator: $\frac{15.0}{4.00}=3.75$ seconds. Time cannot be negative in this context as the velocity is increasing, so we discard the negative options.

Answer:

C. 3.75 seconds