Chapter 4, Problem 75A

To determine

To identify: Whether the assumption of constant acceleration holds true for the given situation or not. Also, to specify the information required to identify whether the acceleration was constant or not.

Answer to Problem 75A

No, the assumption for the constant acceleration does not hold true.

The information of velocities is required. The velocities should be equal in equal interval of time for constant acceleration.

Explanation of Solution

Given:

Dragster completed 402.30 m track in 4.936 s.

Formula:

The equation of motion is,

  $\begin{array}{l}s=ut+\frac{1}{2}a{t}^2\\ d_f-d_i=ut+\frac{1}{2}a{t}^2\end{array}$

Where d_f and d_i are the final and initial displacement of dragster

Calculation:

Initially, the displacement and velocity is zero. So,

  $\begin{array}{l}{d}_i=0\\ u=0\text{m}/\text{s}\end{array}$

So,

  $\begin{array}{l}{d}_f=0+\frac{1}{2}a{t}^2\\ 402.3=\frac{1}{2}a{\left(4.936\right)}^2\\ a=33.02{\text{m/s}}^{\text{2}}\end{array}$

To find the final velocity,

  $\begin{array}{l}a=\frac{dv}{dt}=\frac{v_f-v_i}{t_f--t_i}\\ =\frac{v_f-0}{4.936-0}\\ v_f=162.98\text{m/s}\end{array}$

The value of velocity obtained is higher than the provided one, so the acceleration is no longer constant and the assumption does not hold true. For a constant acceleration, velocities value should be same in equal interval of time.