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.
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