Q2.5-37PE - College Physics (Urone)

Question

Dragsters can actually reach a top speed of  in only  considerably less time than given in Example 2.10 and Example 2.11. 

(a) Calculate the average acceleration for such a dragster. 

(b) Find the final velocity of this dragster starting from rest and accelerating at the rate found in (a) for 402 m (a quarter mile) without using any information on time. 

(c) Why is the final velocity greater than that used to find the average acceleration? 

Hint: Consider whether the assumption of constant acceleration is valid for a dragster. If not, discuss whether the acceleration would be greater at the beginning or end of the run and what effect that would have on the final velocity.

Step-by-Step Solution

Answer

a) 32.6 m/s²

b) 162 m/s

c) The acceleration is strongest in the first few gears and gradually decreases as the gears are increased. 

Given data

• Intial velocity U = 0.
• Final velocity V = 145.
• The taken to reach final velocity T = 4.45 s.

Average acceleration

a)

Now to calculate the acceleration, we have the equation of acceleration

$\mathbf{a}\mathbf{=}\frac{\mathbf{V}\mathbf{-}\mathbf{U}}{\mathbf{T}}$

Here V is the final velocity, and U is the initial velocity.

Substituting values in the above expression, we get,

$$\begin{gathered} a=\frac{145-0}{4.45} \\ a=32.6 {\text{m/s}}^{\text{2}} \end{gathered}$$

Hence the average acceleration of the dragster is 32.6 m/s².

Final velocity of dragster

b)

Data given is:

Distance d = 402.

The dragster's final velocity  can be calculated from the equation of motion as:

$V^2-U^2=2ad$

Here V is the final velocity, U is the initial velocity, a is the acceleration, and d is the traveled distance.

Substituting values in the above expression, we get,

$$\begin{gathered} V^2-0^2=2\times 32.6\times 402 \\ V=162 \text{m/s} \end{gathered}$$

Hence the final velocity is .

c)

For a dragster, the constant acceleration assumption is invalid. 

Various gears on a dragster have different acceleration rates. 

The acceleration is strongest in the first few gears and gradually decreases as the gears are increased. 

As a result, it would accelerate at a slower pace than in the previous few meters, with a final velocity of less than 162 m/s.