Question

a bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 m. determine the acceleration of the bike.

Answer 1

Question #57373, Physics / Mechanics | Relativity

a bike accelerates uniformly from rest to a speed of $7.10 \, \text{m/s}$ over a distance of $35.4 \, \text{m}$ determine the acceleration of the bike.

Solution:

Displacement during the uniformly accelerated motion:

$$d = \frac {a t ^ {2}}{2};$$

Speed reached during the uniformly accelerated motion (if object started from rest):

$$v = a t;$$

Solving (1) and (2) for $t^2$:

$$t ^ {2} = \frac {2 d}{a};$$ $$t ^ {2} = \frac {v ^ {2}}{a ^ {2}};$$

Combining (3) and (4):

$$\frac {2 d}{a} = \frac {v ^ {2}}{a ^ {2}};$$ $$2 d = \frac {v ^ {2}}{a};$$

And solving for $a$:

$$a = \frac {v ^ {2}}{2 d};$$ $$a = \frac {7.10 ^ {2}}{2 \times 35.4} = 0.712 \, \text{m/s}^2$$

Answer: the bike's acceleration is $0.712 \, \text{m/s}^2$

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