A body of mass 2 kg travels along x axis, such that its position as a function of time is given by X(t) = at ßt2 + 7, where a = 3 m/s, B = 2 m/s² and 7 = 4 myst. The force acting on the body at time t = 3 s is
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ANSWER IS HERE:-
, m=2kgm=2kg
x(t)=pt+qt2+rt3x(t)=pt+qt2+rt3
υ=dxdt=p+2qt+3rt2υ=dxdt=p+2qt+3rt2
a=dυdt=0+2q+6rta=dυdt=0+2q+6rt
As t=2sec,a=2q+12r=2×4+12×5=6/s2t=2sec,a=2q+12r=2×4+12×5=68m/s2
F=ma=2×68N=136NF=ma=2×68N=136N .
Given that,
mass of body = m = 2kg
Position of body wrt time = X(t) = at + Bt² + 7
To find net force.
According to Newton's Laws of motion, The behaviour of objects for which all existing forces are not balanced is described by Newton's second law of motion. According to the second law, an object's acceleration is determined by two variables: the net force acting on the object and the mass of the item. The acceleration of an item is proportional to the net force exerted on it and inversely proportional to its mass.
The acceleration of an item increases in proportion to the force applied on it. The acceleration of an item decreases as the mass of the thing increases.
Therefore, differentiating the funtion of position X(t) wrt time, we'll get velocity.
∴ v = a + Bt
Differentiating the velocity equation wrt time we'll get acceleration of the body.
∴ a = B
∴ Acceleration on the body is consant as B = 3 m/s²
∴ The force acting on the body at all time remains constant.
∴ Force acting on body = m × a at time t
∴ Force acting on body = 2 × 2
∴ Force acting on body = 4 N