A motorbike accelerates from 15 m/s to 25 m/s in 15 seconds. How far does the motorbike travel in this time? Give your answer to three significant figures.
Yikes !
= 15 * 15 +(1/2)(2/3) * 15^2
= 225 + 75 = 300 meters
or just say average speed = (15 + 25) / 2 = 40/2 = 20 m/s
20 m/s * 15 s = 300 meters
I am getting kind of sleepy.
To find the distance traveled by the motorbike, we can use the equation:
distance = initial velocity × time + 0.5 × acceleration × time²
In this case, the initial velocity (u) is 15 m/s, the final velocity (v) is 25 m/s, and the time (t) is 15 seconds. We need to calculate the distance (s). But first, we need to determine the acceleration (a).
The acceleration can be calculated using the formula:
acceleration = (final velocity - initial velocity) / time
Plugging in the given values, we have:
acceleration = (25 m/s - 15 m/s) / 15 s
acceleration = 10 m/s / 15 s
acceleration ≈ 0.67 m/s² (rounded to two decimal places)
Now that we have the acceleration, we can find the distance:
distance = 15 m/s × 15 s + 0.5 × 0.67 m/s² × (15 s)²
distance ≈ 225 m + 0.5 × 0.67 m/s² × 225 s²
distance ≈ 225 m + 0.5 × 0.67 m/s² × 50625 s²
distance ≈ 225 m + 0.335 m/s² × 50625 s²
distance ≈ 225 m + 16968.75 m
distance ≈ 17193.75 m
Rounding the answer to three significant figures, the motorbike travels approximately 17.2 km (kilometers) in 15 seconds.
v = Vi + a t
25 = 15 + a * 15
a = 10/15 = (2/3) m/s^2
d = Vi t + (1/2) a t^2
= 15 * 15 +(1/2)(2/3) * 15^2
= 30 + 75 = 105 meters