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

Answer:

A. $2\cdot t$

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:

$\frac{v_{1}}{t_{1}} = \frac{v_{2}}{t_{2}}$ (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:

$\frac{v}{t} = \frac{2\cdot v}{t_{2} }$

$t_{2} = 2\cdot t$

Hence, correct answer is A.