Question

A bike first accelerates from 0.0 m/s to 5.0 m/s in 4.5s, then continues at this constant speed for another 4.5 s. What is the total distance traveled by the bike?

Answer 1

Hello!

A bike first accelerates from 0.0 m/s to 5.0 m/s in 4.5 s, then continues at this constant speed for another 4.5 s. What is the total distance traveled by the bike ?

* Determine the acceleration of the bike....

We have the following data:

Vf (final velocity) = 5.0 m/s

Vi (initial velocity) = 0 m/s

ΔV  (speed interval)  = Vf - Vi → ΔV  = 5 - 0 → ΔV  = 5 m/s

ΔT (time interval) = 4.5 s

a (average acceleration) = ? (in m/s²)

Formula:

$\boxed{a = \dfrac{\Delta{V}}{\Delta{T^}}}$

Solving:  

$a = \dfrac{\Delta{V}}{\Delta{T^}}$

$a = \dfrac{5\:\dfrac{m}{s}}{4.5\:s}$

$\boxed{a \approx 1.111\:m/s^2}}\longleftarrow(acceleration)$

* The total distance traveled ?

We have the following data:

Vi (initial velocity) = 0 m/s

t (time) = 4.5 s

a (average acceleration) = 1.111 m/s²

d1 (distance traveled) = ? (in m)

By the formula of the space of the Uniformly Varied Movement, it is:

$d_1 = v_i * t + \dfrac{a*t^{2}}{2}$

$d_1 = 0 * 4.5 + \dfrac{1.111*(4.5)^{2}}{2}$

$d_1 = 0 + \dfrac{1.111*20.25}{2}$

$d_1 = \dfrac{22.49775}{2}$

$\boxed{d_1 \approx 11.25\:m}\longleftarrow(distance)$

* Then continues at this constant speed for another 4.5 s, then:

datos:

d2 (distance traveled) = ? (in m)

s (speed) = 5.0 m/s (constant speed)

t (time) = 4.5 s

Solving:

$s = \dfrac{d_2}{t}$

$d_2 = s*t$

$d_2 = 5\:\dfrac{m}{\diagup\!\!\!\!s} *4.5\:\diagup\!\!\!\!s$

$\boxed{d_2 = 22.5\:m}\longleftarrow(distance)$

* Therefore, what is the total distance traveled by the bike?

$d_{total} = d_1 + d_2$

$d_{total} = 11.25\:m+ 22.5\:m$

$\boxed{\boxed{d_{total} = 33.75\:m}}\:\:\:\:\:\:\bf\purple{\checkmark}$

Answer:

The total distance traveled is 33.75 meters

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Answer 2

Assuming constant acceleration, the distance travelled in the first 4.5s is:

0.5*5.0*4.5 = 11.25m

The distance travelled in the next 4.5s is:

5.0*4.5 = 22.5m

The total distance travelled is:

11.25 + 22.5 = 33.75m