A jogger starting morning run accelerates from a stand still to their jogging pace of 8km/hr. They reach a speed of 8km/hr 5 seconds after starting. How long does it take the jogger to reach the end of their 20m driveway?
V = 8km/h = 8000m/3600s = 2.22m/s.
0.5a = (V-Vo)/t = (2.22-0)/5 = 0.444 m/s^2
d = 0.5a*t^2 = 20 m.
0.222*t^2 = 20
t^2 = 90.1
t = 9.49 s.
To find the time it takes for the jogger to reach the end of their 20m driveway, we can break down the problem into two parts: finding the time it takes for the jogger to reach a constant speed and then finding the time it takes to cover the distance at that constant speed.
First, let's find the time it takes for the jogger to reach a constant speed of 8km/hr. We know that the jogger accelerates from a standstill to 8km/hr in 5 seconds. Therefore, we have an initial velocity of 0 km/hr, final velocity of 8 km/hr, and a time of 5 seconds. We can use the formula:
acceleration = (final velocity - initial velocity) / time
In this case, the acceleration is equal to:
acceleration = (8 km/hr - 0 km/hr) / 5 s
Simplifying this equation, we get:
acceleration = 8 km/hr / 5 s = 1.6 km/hr/s
Now, let's find the time it takes for the jogger to cover the distance of 20m at a constant speed of 8 km/hr. We can use the formula:
time = distance / speed
In this case, the distance is 20m and the speed is 8 km/hr. However, we need to convert the speed to m/s to match the units of the distance. We know that 1 km/hr is equal to 1000m/3600s, so:
speed = 8 km/hr * (1000 m / 3600s) = (8 * 1000) m / (3600s) = 2.2222... m/s (approx.)
Now, we can substitute the values into the formula:
time = 20m / 2.2222... m/s
Calculating this equation, we find:
time ≈ 9.0009... seconds (approx.)
Therefore, it takes approximately 9 seconds for the jogger to reach the end of their 20m driveway.