Free TCE Physics Flashcard Review
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What does the gradient of a displacement–time graph give?
The velocity. A curved s–t graph means the velocity is changing, and the gradient of the tangent gives the instantaneous velocity.
What does the area under a velocity–time graph give?
The displacement. Areas below the time axis count as negative displacement; adding their sizes instead gives the distance travelled.
What does the gradient of a velocity–time graph give?
The acceleration. A straight v–t line means constant (uniform) acceleration.
State the four equations of uniformly accelerated motion.
v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t. They apply only when the acceleration is constant.
How do you add two displacement vectors that are not at right angles?
Draw them head to tail and close the triangle; find the resultant's size with the cosine rule and its direction with the sine rule (or add x and y components).
What is terminal velocity?
The constant velocity reached by a falling object when air resistance has grown to equal its weight, so the net force and acceleration are zero.
A car slows from 25 m s⁻¹ to rest in 5.0 s. What is its acceleration?
a = (v − u)/t = (0 − 25)/5.0 = −5.0 m s⁻²; that is, 5.0 m s⁻² opposite to the motion.
Why must km h⁻¹ be converted before using the motion equations?
The equations need consistent SI units; divide km h⁻¹ by 3.6 to get m s⁻¹ (e.g. 90 km h⁻¹ = 25 m s⁻¹).
What is the difference between distance and displacement?
Distance is the scalar length of the path travelled; displacement is the vector change in position, from start to finish, with a direction.
What sign convention problems arise in vertical motion?
Choose one direction as positive and keep it: if up is positive, g = −9.81 m s⁻² and any displacement below the launch point is negative.
Why are the horizontal and vertical motions of a projectile treated separately?
They are independent: with no air resistance there is no horizontal force (constant horizontal velocity), while gravity gives a constant vertical acceleration of 9.81 m s⁻² down.
What is the vertical velocity of a projectile at the top of its path?
Zero. The horizontal velocity is unchanged, so the speed at the top equals the horizontal component u cos θ.
How do you find the time of flight for a projectile landing lower than its launch point?
Solve s = u_y t + ½at² for t using the (negative) vertical displacement to the landing point; take the positive root of the quadratic.
What launch angle gives the maximum range on level ground (no air resistance)?
45°. Complementary angles such as 30° and 60° give equal ranges at the same launch speed.
How do you find the speed and direction of a projectile just before landing?
Find v_x (unchanged) and v_y = u_y + at; speed = √(v_x² + v_y²) and the angle below the horizontal is tan⁻¹(|v_y|/v_x).
A ball rolls off a 1.25 m high table at 3.0 m s⁻¹. How far from the table does it land?
t = √(2h/g) = √(2 × 1.25/9.81) = 0.505 s; range = 3.0 × 0.505 = 1.5 m.
Two objects are released at the same time from the same height: one dropped, one thrown horizontally. Which lands first?
They land together: both start with zero vertical velocity and have the same vertical acceleration.
What shape is the path of a projectile without air resistance?
A parabola, because horizontal displacement grows linearly with time while vertical displacement depends on t².
How does air resistance change a projectile's path?
It reduces both the range and the maximum height, and the descent becomes steeper than the ascent; the path is no longer a symmetric parabola.
Give the formula for the maximum height reached by a projectile above its launch point.
h = u_y²/(2g), where u_y = u sin θ is the vertical component of the launch velocity.