The engine of a motorcycle can produce a maximum acceleration 5 meters per second square. Its brakes can produce a maximum retardation 10meters per second square. What is the minimum time in which it can cover a distanceof 1.5km
30
To find the minimum time it takes for the motorcycle to cover a distance of 1.5 km, we need to calculate the time it takes to accelerate to full speed and then the time it takes to decelerate to a stop.
First, let's calculate the time it takes to accelerate to full speed.
Given:
Maximum acceleration (a) = 5 m/s^2
Distance (d) = 1.5 km = 1500 m
We can use the kinematic equation: v^2 = u^2 + 2ax, where:
v = final velocity
u = initial velocity (assumed to be 0 m/s, as the motorcycle starts from rest)
a = acceleration
x = distance
Rearranging the equation, we have: v = sqrt(2ax)
Substituting the given values, we get: v = sqrt(2 * 5 * 1500)
Calculating this, we find: v ≈ sqrt(15000) ≈ 122.47 m/s
Now, let's calculate the time it takes to accelerate to full speed. We'll use the equation: t = (v - u) / a, where u = 0.
Substituting the values, we get: t = (122.47 - 0) / 5
Calculating this, we find: t ≈ 24.49 seconds (approximately)
Next, let's calculate the time it takes to decelerate to a stop.
Given:
Maximum retardation (a') = -10 m/s^2 (negative sign as it represents deceleration)
Distance (d') = 1500 m
Using the same kinematic equation: v^2 = u^2 + 2ax, but here, the final velocity (v) will be 0 m/s.
So, the equation becomes: u^2 = 2 * a' * x'
Substituting the given values, we get: 0^2 = 2 * (-10) * 1500
Simplifying this, we find: 30000 = -30000
Since the equation doesn't hold true, it means that the motorcycle cannot decelerate to a stop within the given distance and given maximum retardation. Therefore, it will not come to a complete stop within 1500 m.
Overall, the total time it takes for the motorcycle to travel 1.5 km will be the time taken to accelerate to full speed, which is approximately 24.49 seconds. However, please note that the motorcycle will not come to a complete stop within this distance.
d = 0.5a*t^2 = 1500 m.
2.5*t^2 = 1500, t = 24.5 s.