View all 15 cards in this deck

#	Question	Answer
1	What is instantaneous velocity?	The limit of the average velocity as the time interval \(\Delta t\) becomes infinitesimally small: \( v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt} \).
2	What is average acceleration?	The change of velocity divided by the time interval: \( \bar{a} = \frac{\Delta v}{\Delta t} \).
3	What is the relation between displacement and time for uniformly accelerated motion?	\( x = v_0 t + \frac{1}{2} a t^2 \).
4	What is the general kinematic equation relating velocity and displacement when the initial position is \( x_0 \)?	\( v^2 = v_0^2 + 2 a (x - x_0) \).
5	How does the stopping distance of a vehicle depend on its initial velocity?	It is proportional to the square of the initial velocity.
6	What does the area under a velocity-time graph between times \( t_1 \) and \( t_2 \) represent?	The displacement of the object during that interval of time.
7	When is acceleration in the same direction as velocity?	When the particle is speeding up.
8	Is the magnitude of average velocity always equal to the average speed over the same interval?	No. Average speed is greater than or equal to the magnitude of average velocity. Equality holds only when the particle moves in a straight line without changing direction.
9	A man walks to a market 2.5 km away at 5 km h⁻¹ and returns at 7.5 km h⁻¹. What is the magnitude of his average velocity for the whole journey?	Zero (displacement is zero).
10	For the same particle (\( x = a + bt^2 \), \( b = 2.5\,\mathrm{m\,s^{-2}} \)), what is its average velocity between \( t = 2.0\,\mathrm{s} \) and \( t = 4.0\,\mathrm{s} \)?	\( 15\,\mathrm{m\,s^{-1}} \).
11	How does the curvature of a position-time graph indicate the sign of acceleration?	The graph curves upward for positive acceleration, curves downward for negative acceleration, and is a straight line for zero acceleration.
12	Before assigning signs to displacement, velocity, and acceleration, what must first be specified?	The origin and the positive direction of the axis — both are a matter of choice.
13	A man walks to a market 2.5 km away at 5 km h⁻¹ and returns at 7.5 km h⁻¹. What are the magnitude of his average velocity and his average speed over the interval 0 to 30 minutes?	Both are 5 km h⁻¹ (he is still on the outward leg, reaching the market exactly at \( t = 30\,\mathrm{min} \), so path length equals the magnitude of displacement).
14	A particle's displacement is \( s = t^3 - 6t^2 + 3t + 4 \) (SI units). Using \( v = ds/dt \) and \( a = dv/dt \), what is its velocity at the instant its acceleration is zero?	\( -9\,\mathrm{m\,s^{-1}} \) — acceleration \( a = 6t - 12 \) is zero at \( t = 2\,\mathrm{s} \); velocity there is \( v = 3t^2 - 12t + 3 = -9\,\mathrm{m\,s^{-1}} \).
15	A particle covers each of three equal parts of a distance at 20 m s⁻¹, 40 m s⁻¹, and 60 m s⁻¹ respectively. What is its average speed for the whole journey?	Approximately 32.7 m s⁻¹ (exactly \( 360/11\,\mathrm{m\,s^{-1}} \)), from total path length divided by total time.