A 2,200-lb sports car with a power of 135 hp can accelerate from zero to 110 mph. How long approximately will it take to accomplish this?

A. 6.3 sec
B. 13 sec
C. 17 sec
D. 21 sec
E. 26 sec

Question

High School

We appreciate your visit to A 2 200 lb sports car with a power of 135 hp can accelerate from zero to 110 mph How long approximately will it take. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Answer :

ikarikayah ikarikayah · Answer 1 · 2024-05-17T00:08:50-04:00

The sports car takes approximately 24 seconds to accelerate from zero to 110 mph, which is closest to option (e) 26 seconds.

To find the approximate time it takes for the car to accelerate from 0 to 110 mph, we can use the equation:

[tex]\[ \text{Time} = \frac{\text{Final Velocity} - \text{Initial Velocity}}{\text{Acceleration}} \][/tex]

First, we need to convert the car's weight from pounds to mass in kilograms:

[tex]\[ \text{Mass} = \frac{2200 \text{ lb}}{2.20462 \text{ lb/kg}} \approx 997.9 \text{ kg} \][/tex]

Now, we need to find the acceleration. We can use the formula:

[tex]\[ \text{Power} = \text{Force} \times \text{Velocity} \][/tex]

Rearranging for force:

[tex]\[ \text{Force} = \frac{\text{Power}}{\text{Velocity}} \][/tex]

Using the power of 135 hp (which is approximately 100.7 kW) and the velocity in m/s (110 mph converted to m/s):

[tex]\[ \text{Velocity} = \frac{110 \text{ mph} \times 1609.34 \text{ m/mile}}{3600 \text{ s/h}} \approx 49.17 \text{ m/s} \][/tex]

[tex]\[ \text{Force} = \frac{100.7 \text{ kW}}{49.17 \text{ m/s}} \approx 2.05 \text{ kN} \][/tex]

Now, we can find acceleration using Newton's second law (\( F = ma \)):

[tex]\[ \text{Acceleration} = \frac{\text{Force}}{\text{Mass}} \][/tex]

[tex]\[ \text{Acceleration} = \frac{2.05 \text{ kN}}{997.9 \text{ kg}} \approx 2.05 \text{ m/s}^2 \][/tex]

Finally, we can find the time using the equation:

[tex]\[ \text{Time} = \frac{\text{Final Velocity} - \text{Initial Velocity}}{\text{Acceleration}} \][/tex]

[tex]\[ \text{Time} = \frac{49.17 \text{ m/s} - 0}{2.05 \text{ m/s}^2} \approx 23.96 \text{ s} \][/tex]

Rounded to the nearest whole number, the time is approximately 24 seconds, which is closest to option (e) 26 seconds.

Complete question:

A 2,200-lb sports car with a power of 135 hp can accelerate from zero to 110 mph. How long approximately will it take to accomplish this?

a. 6.3 sec

b. 13 sec

c. 17 sec

d. 21 sec

e. 26 sec