TOPIC-2
- Acceleration
- Acceleration is defined as the rate of change of velocity with time.
- Acceleration is a vector quantity.
- SI unit of acceleration is \(m/{s^2}\) .
Average acceleration
- Average acceleration is defined as the ratio of change in velocity over a time interval to the time interval.
- If a particle moving along a straight line has velocity \({V_1}\) at an instant \({t_1}\) and velocity \({V_2}\) at instant \({t_2}\) ,then average acceleration during time interval \({t_2} - {t_1}\) is given by \({a_{avg}} = \frac{{\Delta v}}{{\Delta t}} = \frac{{{V_2} - {V_1}}}{{{t_2} - {t_1}}}\)
Summary of equations for uniformly accelerated motion.
- \(v = u + at\) . . . Eq. I
- \(s = ut + \frac{1}{2}a{t^2}\) . . . Eq. II
- \(x - {x_0} = ut + \frac{1}{2}a{t^2}\) . . . Eq. III
- \({v^2} = {u^2} + 2as\) . . . Eq. IV
- \({v^2} = {u^2} + 2a\left( {x - {x_0}} \right)\) . . . Eq. V
- \(s = \left( {\frac{{u + v}}{2}} \right) \times t\) . . . Eq. VI
Where
u - Initial velocity or instantaneous velocity at time t = 0
v - Instantaneous velocity at time instant t
a - uniform acceleration
s- Displacement at time t
t - Time instant
\({{x_0}}\) - Initial position or position at t = 0.
x-Position at time t
\({S_{{n^{th}}}}\)-Displacement in \({{n^{th}}}\) second
Equations for uniformly accelerated motion in vector form.
- \(\vec v = \vec u + \vec at\)
- \(\vec s = \vec ut + \frac{1}{2}\vec a{t^2}\)
- \(\vec v \bullet \vec v = \vec u \bullet \vec u + 2\vec a \bullet \vec s\)
- \(\vec s = \left( {\frac{{\vec u + \vec v}}{2}} \right) \times t\)