A sports car accelerates from rest to 86km/h\, km/h in 5.2s\, s . What is its average acceleration in m/s2{\rm{m/s}}^2.
V = 86km/h = 86000m/3600s = 23.89 m/s.
a=(V-Vo)/t = (23.89-0)/5.2 = 4.59 m/s^2
To find the average acceleration of the sports car, we need to use the formula:
\[ \text{Average Acceleration} = \frac{\text{Change in Velocity}}{\text{Time elapsed}} \]
First, we need to convert the given velocity from kilometers per hour to meters per second, as the standard SI unit for velocity is meters per second.
Given: Initial velocity (u) = 0 km/h
Final velocity (v) = 86 km/h
Time (t) = 5.2s
To convert the velocities from km/h to m/s, we use the conversion factor:
1 km/h = 0.2778 m/s
So, the initial velocity (u) in m/s is:
\[ u = 0 \times 0.2778 = 0 \, \text{m/s} \]
And the final velocity (v) in m/s is:
\[ v = 86 \times 0.2778 = 23.888 \, \text{m/s} \]
Now we can calculate the change in velocity (Δv):
\[ \Delta v = v - u = 23.888 \, \text{m/s} - 0 \, \text{m/s} = 23.888 \, \text{m/s} \]
Finally, we can calculate the average acceleration (a):
\[ a = \frac{\Delta v}{t} = \frac{23.888 \, \text{m/s}}{5.2 \, \text{s}} \approx 4.6 \, \text{m/s}^2 \]
Therefore, the average acceleration of the sports car is approximately 4.6 m/s².