A driver in a car traveling at a speed of
79 km/h sees a cat 107 m away on the road.
How long will it take for the car to accelerate uniformly to a stop in exactly 103 m?
Answer in units of s
To solve this problem, we can use the kinematic equation that relates the initial velocity (v₀), final velocity (v), acceleration (a), and distance (d):
v^2 = v₀^2 + 2ad
First, let's convert the speed from km/h to m/s:
Speed = 79 km/h = 79 * (1000 m / 1 km) / (3600 s / 1 h) = 21.94 m/s
Given:
Initial velocity (v₀) = 21.94 m/s
Distance (d) = 103 m
Final velocity (v) = 0 m/s (since the car will come to a stop)
Acceleration (a) = ?
Plugging these values into the kinematic equation, we have:
0^2 = (21.94)^2 + 2a(103)
Simplifying:
0 = 480.6436 + 206a
Rearranging the equation to solve for acceleration (a):
-206a = 480.6436
a = 480.6436 / -206
a ≈ -2.336 m/s^2
Given the negative sign, it means the car is decelerating or accelerating in the opposite direction of the initial velocity.
Next, we can use the formula for the time it takes to accelerate uniformly from one velocity to another:
t = (v - v₀) / a
Plugging in the values:
t = (0 - 21.94) / -2.336
t ≈ 9.4 seconds
Therefore, it will take approximately 9.4 seconds for the car to accelerate uniformly to a stop in exactly 103 m.