A car is running at 15m/s when the driver decides to accelerate in order to reach a speed of 45m/s over a 200m. (a) calculate the time (b) the acceleration

1 answer

To calculate the time:

Using the equation of motion:

\(v = u + at\),

where:
v = final velocity = 45 m/s,
u = initial velocity = 15 m/s,
a = acceleration,
t = time.

Rearranging the equation:

\(t = \frac{{v - u}}{a}\).

Given the values:

\(v = 45\) m/s,
\(u = 15\) m/s.

To find the time, we need to calculate the acceleration (a) first.

To calculate the acceleration:

We can use the equation of motion:

\(v^2 = u^2 + 2as\),

where:
v = final velocity = 45 m/s,
u = initial velocity = 15 m/s,
a = acceleration,
s = distance traveled = 200 m.

Rearranging the equation:

\(a = \frac{{v^2 - u^2}}{2s}\).

Given the values:

\(v = 45\) m/s,
\(u = 15\) m/s,
\(s = 200\) m.

(a) Calculating the acceleration:
\(a = \frac{{45^2 - 15^2}}{2 \cdot 200}\).

\(a = \frac{{2025 - 225}}{400}\).

\(a = \frac{{1800}}{400}\).

\(a = 4.5 \, \text{m/s}^2\).

(b) Calculating the time:
\(t = \frac{{45 - 15}}{4.5}\).

\(t = \frac{{30}}{4.5}\).

\(t = 6.67\) seconds (approximately).

Therefore, the time taken to reach a speed of 45 m/s is approximately 6.67 seconds, and the acceleration is 4.5 m/s^2.