Question

An SUV is accelerated from rest to a speed v in a time interval t. Neglecting air resistance effects and assuming the engine is operating at its maximum power rating when accelerating, determine the time interval for the SUV to accelerate from rest to a speed 2v.

a. 2t
b. 4t
c. 2.5t
d. 3t

Answer 1

To determine the time interval for the SUV to accelerate from rest to a speed 2v, we can use the equation for uniform acceleration and dividing both sides by a, we get t = 2v/a. Therefore, the correct answer is 2t.

Step-by-step explanation:

To determine the time interval for the SUV to accelerate from rest to a speed 2v, we can use the equation for uniform acceleration:

v = u + at

Where v is the final velocity, u is the initial velocity (0 m/s since the SUV starts from rest), a is the acceleration, and t is the time interval.

Since the engine is operating at its maximum power rating, the acceleration will remain constant.

Using this equation, we can write:

2v = 0 + at

Since v = 2v, we have:

2v = at

Dividing both sides by a, we get:

t = 2v/a

Therefore, the correct answer is 2t.

Answer 2

A.
`2\cdot t`

Step-by-step explanation:

The SUV accelerates uniformly. In this case, speed (
`v`) is directly proportional to time (
`t`). That is:

`v \propto t` (1)

`v = k\cdot t`

Where
`k` is the proportionality constant.

Then, we eliminate this constant by creating the following relationship:

`(v_(1))/(t_(1)) = (v_(2))/(t_(2))` (2)

If we know that
`v_(1) = v`,
`t_(1) = t` and
`v_(2) = 2\cdot v`, then the time interval for the SUV to accelerate from rest to a speed
`2\cdot v` is:

`(v)/(t) = (2\cdot v)/(t_(2) )`

`t_(2) = 2\cdot t`

Hence, correct answer is A.