Question

The maker of an automobile advertises that it takes 12 seconds to accelerate from 20 kilometers per hour to 65 kilometers per hour. Assuming constant acceleration, compute the acceleration in meters per second per second. Round your answer to three decimal places.

Answer 1

Answer:

The acceleration is 1.0416 m/$s^{2}$

Step-by-step explanation:

In order to solve this problem we first need to know the formula for acceleration which is the following.

$acceleration = \frac{final.velocity - initial.velocity}{final.time - initial.time}$

Since the time acceleration is calculated as $m/s^{2}$ we need to convert the km/h into m/s. Since 1km = 1000m and 1 hour = 3600 seconds, then

$\frac{20*1000 }{3600s} = \frac{20,000m}{3600s} = \frac{20m}{3.6s}$

**Dividing numerator and denominator by 1000 to simplify**

$\frac{65*1000 }{3600s} = \frac{65,000m}{3600s} = \frac{65m}{3.6s}$

**Dividing numerator and denominator by 1000 to simplify**

Now we can plug in the values into the acceleration formula to calculate the acceleration.

$acceleration = \frac{\frac{65m}{3.6s}-\frac{20m}{3.6s} }{12s-0s}$

$acceleration = \frac{\frac{45m}{3.6s}}{12s}$

$acceleration = \frac{\frac{12.5m}{s}}{12s}$

$acceleration = \frac{\frac{1.0416m}{s}}{s}$

Finally we can see that the acceleration is 1.0416 m/$s^{2}$