The distance covered by a certain object which is travelling at a certain speed is calculated through the equation,
d = (V₀)t + 0.5at²
where d is the distance, V₀ is the initial speed, a is deceleration, and t is the time. Substituting the known values,
85 = (V₀)(t) + (0.5)(-0.43 m/s)(t²)
Because we are not given with the initial velocity, our answer would
remain as the equation which is written above.
Answer:
Time taken, t = 19.86 seconds
Explanation:
It is given that,
Deceleration of the sled, a = -0.43 m/s²
We have to find the time it take to stop if it travels 85 m before coming to rest i.e final velocity v = 0. Using third equation of motion as :
[tex]v^2-u^2=2as[/tex]
[tex]0-u^2=2\times (-0.43\ m/s^2)\times 85\ m[/tex]
u = 8.54 m/s
The initial velocity of the sled is 8.54 m/s. For finding time taken by the sled to stop can be calculated using second equation of motion as :
[tex]s=ut+\dfrac{1}{2}at^2[/tex]
[tex]85=8.54t+\dfrac{1}{2}\times (-0.43)t^2[/tex]
[tex]0.215t^2-8.54t+85=0[/tex]
On solving the above quadratic equation we get, t = 19.86 seconds. Hence, this is the required solution.
