Starting from rest, a man runs 10 metres along a straight path in t seconds. His position can be described by the function s(t)=0.7t^2. How long will it take him to reach the velocity of 4m/s?
would the answer be 5.6 s? I started with s(t)=0.7t^2, then the velocity is 7/5t and then I substituted 4 into t.
s = .7 t^2
ds/dt = v = 1.4 t
4 = 1.4 t
t = 4/1.4 = 2.86 seconds
It asked for t given v = 4 m/s
thanks!
To find the time it takes for the man to reach a velocity of 4 m/s, we first need to determine the formula for velocity, v(t), based on the given position function, s(t) = 0.7t^2.
The velocity is the derivative of the position function with respect to time, which can be found by differentiating s(t) with respect to t:
v(t) = d/dt (0.7t^2)
= 1.4t
Now, we can set up an equation to find the time it takes for the man to reach a velocity of 4 m/s:
4 = 1.4t
Solving for t:
t = 4 / 1.4
t ≈ 2.857
Therefore, it will take the man approximately 2.857 seconds to reach a velocity of 4 m/s, not 5.6 seconds as you stated.
To determine the time it will take for the man to reach a velocity of 4 m/s, you need to find the time when the velocity function equals 4.
Let's start with the position equation, s(t) = 0.7t^2. To find the velocity, we need to differentiate the position function with respect to time (t).
Taking the derivative of s(t) = 0.7t^2 gives us v(t), the velocity function: v(t) = 1.4t.
Now, we need to find the time (t) when the velocity is 4 m/s. Setting v(t) = 4 and solving for t:
1.4t = 4
t = 4 / 1.4
t ≈ 2.857 seconds
So, it will take approximately 2.857 seconds for the man to reach a velocity of 4 m/s, not 5.6 seconds as you mentioned.