The movement of the body is given by the equation x = 60 5t-10t ^ 2. Initial speed of body movement

The movement of the body is given by the equation x = 60 5t-10t ^ 2. Initial speed of body movement =? its acceleration =? displacement in 1 s =?

Moving in 1 s (t = 1 s):

S = x (1) = 60 + 5t – 10t ^ 2 = 60 + 5 * 1 – 10 * 12 = 60 + 5 – 10 = 55 m.

To find the speed of a body from the function x (t) = 60 + 5t – 10t ^ 2, you need to take the derivative:

x ‘= S’ = V = 0 + 5 * 1 – 10 * 2t = 5 – 20t.

Initial speed of movement (t = 0 s):

V = 5 – 20 * 0 = 5 m / s.

To find the acceleration of a body from the function x (t) = 60 + 5t – 10t ^ 2, it is necessary to take the double derivative (second-order derivative):

x ” = S ” = V ‘= a = (5 – 20t)’ = -20 m / s².