Question

A car travels at a constant speed around a circular track whose radiu is 2.6 km. The goes once arond the track in 360s . What is the magnitude

Answer 1

Answer:

Centripetal acceleration = 0.79 m/s²

Explanation:

Given the following data;

Radius, r = 2.6 km

Time = 360 seconds

Conversion:

2.6 km to meters = 2.6 * 1000 = 2600 meters

To find the magnitude of centripetal acceleration;

First of all, we would determine the circular speed of the car using the formula;

$Circular \; speed (V) = \frac {2 \pi r}{t}$

Where;

• r represents the radius and t is the time.

Substituting into the formula, we have;

$Circular \; speed (V) = \frac {2*3.142*2600}{360}$

$Circular \; speed (V) = \frac {16338.4}{360}$

Circular speed, V = 45.38 m/s

Next, we find the centripetal acceleration;

Mathematically, centripetal acceleration is given by the formula;

$Centripetal \; acceleration = \frac {V^{2}}{r}$

Where;

• V is the circular speed (velocity) of an object.
• r is the radius of circular path.

Substituting into the formula, we have;

$Centripetal \; acceleration = \frac {45.38^{2}}{2.6}$

$Centripetal \; acceleration = \frac {2059.34}{2600}$

Centripetal acceleration = 0.79 m/s²