The rectilinear motion of the body is described by the equation x = 1 + 3t-t ^ 2 to determine the speed
| September 7, 2021 | education
The rectilinear motion of the body is described by the equation x = 1 + 3t-t ^ 2 to determine the speed of acceleration of the body in 4 s.
The speed of a body can be represented as a first-order derivative of the equation of motion of the body. The acceleration of a body can be represented as a second-order derivative of the equation of motion of the body (the first-order derivative of the equation of the body’s velocity).
V (t) = x ‘= (1 + 3t – t ^ 2)’ = 3 – 2t.
At time t = 4 s: V (4) = 3 – 2 * 4 = 3 – 8 = -5 m / s.
a (t) = V ‘= x’ ‘= (1 + 3t – t ^ 2)’ ‘= (3 – 2t)’ = -2 m / s2 (motion is equally slow, acceleration is constant).
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