Physics High School

alexander's hobby is dirt biking. on one occasion last weekend, he accelerated from rest to 12.9 m/s in 4.05 seconds. he then maintained this speed for 8.48 seconds. seeing a coyote run cross the trail ahead of him, he abruptly stops in 5.60 seconds. determine alexander's average speed for this motion.

Answers

Answer 1

Using the equation of motion, it can be determined that Alexander travels at an average speed of 25.57 m/s while operating a bike.

What are motion equations?

Equations of motion are equations that explain how a physical system behaves in terms of how its motion changes over time.

The three equations are,

v = u + at

v² = u² + 2as

s = ut + 1/2at²

Now for the given question,

For the initial 4.05 seconds, initial velocity = 0, acceleration = 12.9 m/s and time taken = 4.05 s

Using first equation of motion,

v = u + at

v = 0 + 12.9(4.05) = 52.245 m/s

He then kept this speed up for 8.48 seconds.

For the last 5.60 seconds, final velocity = 0, initial velocity = 52.245 m/s

Acceleration = (0-52.245)/5.60 = -9.329 m/s

Distance travelled in 4.05 seconds is given as follows:

s = u t + 1/2(at²)

= 0 + 1/2(12.9)(4.05)²

= 105.79 m

Distance travelled in 8.48 seconds = 52.245 × 4.05 = 211.592 m

Distance travelled in 5.60 seconds is given as follows:

s = u t + 1/2(at²)

s = 52.245(5.60) + 1/2(-9.329)(5.60)²

= 146.294 m

Total distance travelled =105.79  + 211.592 + 146.294 = 463.676 m

Average speed = Total distance/Total time = 463.676/(4.05+8.48+5.60)

= 25.57 m/s

Therefore, average motion speed for Alexander while riding a bike is 25.57 m/s which is calculated by using the equation of motion.

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