Question

A cyclist is traveling at 7m s -1, then accelerates at 2.5m s -2 for 15 seconds.
a. How far did they travel during this time?
b. What was the final speed after 15 seconds

Answer 1

Answer:

a) 386.25

b) 44.5 m/s

Explanation:

As per the provided information in the given question, it has been stated that the initial velocity of the cyclist is 7 m/s, acceleration is 2.5 m/s² and time taken is 15 s.

We have,

• Initial velocity (u) = 7 m/s
• Acceleration (a) = 2.5 m/s²
• Time taken (t) = 5 seconds

We've been asked to calculate the distance travelled (s) and the final speed after 15 seconds (v).

In order to calculate the distance travelled, we'll use the 2nd equation of motion.

$\longrightarrow \quad\boxed{ { \textbf{\textsf{ s }} = \textbf{\textsf{ut}} + \dfrac{\textbf{\textsf{ 1 }}}{\textbf{\textsf{2 }}}\textbf{\textsf{at}}^\textbf{\textsf{ 2}} }}$

• s denotes distance
• u denotes initial velocity
• t denotes time
• a denotes acceleration

$\longrightarrow \sf{\quad {s = 7(15) + \dfrac{1}{2} \times 2.5 \times (15)^2 }}$

$\longrightarrow \sf{\quad {s = 105 + \dfrac{1}{2} \times 2.5 \times 225 }}$

$\longrightarrow \sf{\quad {s = 105 + (1.25 \times 225) }}$

$\longrightarrow \sf{\quad {s = 105 + 281.25 }}$

$\longrightarrow \quad \underline{\boxed {\textbf{\textsf{s = 386.25 \; m }}}}$

Now, we have to calculate the final speed after 15 seconds. By using the first equation of motion,

$\longrightarrow \quad\boxed{ { \textbf{\textsf{ v = u + at }} }}$

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• t denotes time

$\longrightarrow \sf{\quad { v = 7 + 2.5(15) }}$

$\longrightarrow \sf{\quad { v = 7 + 37.5 }}$

$\longrightarrow \quad \underline{\boxed {\textbf{\textsf{ v = 44.5 }}\textbf{\textsf{m \: s}}^{{\textbf{\textsf{ -1}}} }}}$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

Therefore,

⠀⠀⠀★ Initial velocity = 386.25 m

⠀⠀⠀★ Final velocity = 44.5 m/s