A car is traveling at 95km/hr. the driver steps on the brakes and the car comes to a stop in 60m. What is the car's deceleration?
Vi = 95,000m/3600 s = 26.4 m/s
v = Vi - a t
v = 0 at end of trip
0 = 26.4 - a t so t = 26.4/a
x = Vi t - .5 a t^2
60 = 26.4 t - .5 a t^2
60 = 26.4 (26.4/a) -.5 (a)(26.4^2)/a^2
60 = .5 (26.4)^2/a
a = 5.8 m/s^2 is deacceleration
To find the car's deceleration, we need to use the formula:
deceleration = (final velocity - initial velocity) / time
In this case, the car came to a stop, so the final velocity is 0 km/hr. The initial velocity is 95 km/hr, and the time it took to come to a stop is not given. However, we can calculate the time using the distance traveled and the initial velocity.
First, we need to convert the initial velocity from km/hr to m/s:
95 km/hr * (1000 m / 1 km) * (1 hr / 3600 s) = 26.39 m/s
Now, we can use the formula:
deceleration = (0 - 26.39) m/s / time
To find the time it took to come to a stop, we can use the formula:
distance = (initial velocity + final velocity) / 2 * time
Since the final velocity is 0, the formula becomes:
distance = (initial velocity) / 2 * time
Rearranging the formula, we get:
time = distance * 2 / initial velocity
Plugging in the values:
time = 60 m * 2 / 26.39 m/s = 4.54 s
Now we can calculate the deceleration:
deceleration = (0 - 26.39) m/s / 4.54 s = -5.80 m/s^2
Therefore, the car's deceleration is approximately -5.80 m/s^2. The negative sign indicates deceleration or slowing down.