A sports car is advertised to be able to stop in a distance of 60 m from a speed of 105 km/h.
(a) What is its acceleration in m/s2?
Incorrect: Your answer is incorrect. m/s2
(b) How many g's is this (g = 9.80 m/s2)?
Correct: Your answer is correct.
Convert the velocity V to m/s.,
V = sqrt(2aX)
X = 60 m,
Solve for a.
a = V^2/(2X)
Divide a in m/s^2 by 9.8 to convert to g's
To calculate the acceleration of the sports car, we can use the formula:
acceleration = (final velocity^2 - initial velocity^2) / (2 * distance)
First, we need to convert the given speed of 105 km/h into m/s. To do this, we multiply it by the conversion factor of 1000 m/1 km and 1 h/3600 s:
105 km/h * (1000 m/1 km) * (1 h/3600 s) = 29.17 m/s
Next, we substitute the values of final velocity (0 m/s, since the car comes to a stop) and distance (60 m) into the formula:
acceleration = (0^2 - 29.17^2) / (2 * 60) = -29.17^2 / 120 = -847.33 / 120 = -7.06 m/s^2
The negative sign indicates deceleration.
Now let's calculate how many g's this acceleration corresponds to. One g is equal to the acceleration due to gravity, which is approximately 9.80 m/s^2.
g-forces = acceleration / (9.80 m/s^2) = -7.06 / 9.80 = -0.72 g
So, the acceleration of the sports car is approximately -7.06 m/s^2, and this corresponds to approximately -0.72 g's.