A 950-kg car is initially travelling at 60 km/hr. If the speed increases so that its kinetic energy increases by 165 kJ, determine the final speed of the car.
change km/hr to m/s
final ke=initialKE+change
then, from the final KE, compute the final speed.
To determine the final speed of the car, we can use the concept of work-energy theorem. The work-energy theorem states that the change in kinetic energy of an object is equal to the net work done on the object.
The initial kinetic energy (KE1) of the car can be calculated using the formula:
KE1 = (1/2) * mass * velocity^2
Given that the mass of the car is 950 kg and the initial velocity is 60 km/hr, we need to convert the initial velocity to meters per second (m/s). We know that 1 km = 1000 m and 1 hr = 3600 s, so:
Initial velocity (v1) = 60 km/hr = (60 * 1000) m / (3600 s) = 16.67 m/s
Substituting the values into the formula, we get:
KE1 = (1/2) * 950 kg * (16.67 m/s)^2 = 138,919 J
Now, we need to find the final kinetic energy (KE2) by adding the increase in kinetic energy (ΔKE) to the initial kinetic energy (KE1):
KE2 = KE1 + ΔKE
Given that ΔKE = 165 kJ = 165,000 J, we have:
KE2 = 138,919 J + 165,000 J = 303,919 J
Using the same formula as before, we can find the final velocity (v2):
KE2 = (1/2) * 950 kg * v2^2
Rearranging the formula, we get:
v2^2 = 2 * (KE2 / mass)
Substituting the values, we have:
v2^2 = 2 * (303,919 J / 950 kg) = 639.86 m^2/s^2
Finally, taking the square root of both sides, we find:
v2 = √(639.86 m^2/s^2) = 25.3 m/s
Therefore, the final speed of the car is approximately 25.3 m/s.