A motorcycle has an initial speed of 40 m/sec. and a constant acceleration of
8 m/sec2
How much time will it take to travel 300 meters?
recall that the distance is given by 40t+4t^2
now solve for 300
i got 5, so it takes 5 seconds to travel 300 meters?
looks good to me
To find out the time it will take for the motorcycle to travel 300 meters, we can use the kinematic equation:
\[ s = ut + \frac{1}{2}at^2 \]
Where:
- s is the distance traveled (300 meters)
- u is the initial speed (40 m/sec)
- a is the constant acceleration (8 m/sec²)
- t is the time taken
Rearranging the equation, we get:
\[ t = \sqrt{\frac{2s}{a}} - \frac{u}{a} \]
Plugging in the values:
\[ t = \sqrt{\frac{2 \times 300}{8}} - \frac{40}{8} \]
Simplifying:
\[ t = \sqrt{75} - 5 \]
Calculating the square root:
\[ t \approx 8.66 - 5 \]
Finally, we get:
\[ t \approx 3.66 \text{ seconds} \]
So, it will take approximately 3.66 seconds for the motorcycle to travel 300 meters with an initial speed of 40 m/sec and a constant acceleration of 8 m/sec².