Motion Basics: 18 flashcards
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1. What is meant by 'motion in a straight line' in physics?
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It is the motion of an object along a straight path without changing direction, where the position changes with time.
2. Define *displacement* and state its SI unit.
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Displacement is the change in position of an object, given by the shortest distance between initial and final points along a straight line. Its SI unit is meter (m).
3. Differentiate between *distance* and *displacement*.
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Distance is the total path length traveled, a scalar quantity. Displacement is the straight-line change in position, a vector quantity. Distance is always positive, while displacement can be positive, negative, or zero.
4. What is *average velocity*? Write its formula.
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Average velocity is the total displacement divided by the total time taken. Formula: $\vec{v}_{avg} = \frac{\Delta x}{\Delta t}$.
5. What is *instantaneous velocity* and how is it calculated?
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Instantaneous velocity is the velocity of an object at a specific instant of time. It is calculated as the limit of average velocity as the time interval approaches zero: $v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt}$.
6. Define *acceleration*. Give its SI unit.
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Acceleration is the rate of change of velocity with respect to time. Its SI unit is meter per second squared ($m/s^2$).
7. Write the three equations of motion for uniformly accelerated motion along a straight line.
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1) $v = u + at$ 2) $s = ut + \frac{1}{2}at^2$ 3) $v^2 = u^2 + 2as$, where $u$ is initial velocity, $v$ is final velocity, $a$ is acceleration, $t$ is time, and $s$ is displacement.
8. What is the slope of a position-time graph?
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The slope of a position-time graph gives the velocity of the object. A steeper slope indicates higher speed.
9. How do you find the displacement from a velocity-time graph?
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The displacement is the area under the velocity-time graph between the time interval of interest.
10. A car accelerates from rest at $2 \, m/s^2$ for 5 seconds. What is its final velocity?
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Using $v = u + at$, with $u = 0$, $a = 2 \, m/s^2$, $t = 5 \, s$, we get $v = 0 + 2 \times 5 = 10 \, m/s$.
11. If an object moves with uniform velocity, what is its acceleration?
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The acceleration is zero because the velocity does not change with time.
12. What does a horizontal line on a velocity-time graph indicate?
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It indicates that the object is moving with constant velocity (zero acceleration).
13. A ball is thrown vertically upward. What is its velocity and acceleration at the highest point?
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At the highest point, the velocity is zero, but the acceleration is still $g$ (approximately $9.8 \, m/s^2$) directed downward.
14. What is the difference between *speed* and *velocity*?
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Speed is the rate of change of distance (scalar), while velocity is the rate of change of displacement (vector). Speed has no direction, velocity has direction.
15. State the condition under which the magnitude of average velocity equals average speed.
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When the object moves along a straight line without changing direction, the distance traveled equals the magnitude of displacement, so average speed equals the magnitude of average velocity.
16. A particle moves along a straight line with position given by $x(t) = 4t^2 - 2t + 1$ (in meters). What is its velocity at $t = 2$ seconds?
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Velocity is the derivative of position: $v(t) = \frac{dx}{dt} = 8t - 2$. At $t = 2$, $v = 8(2) - 2 = 14 \, m/s$.
17. What is the physical meaning of the area under an acceleration-time graph?
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The area under an acceleration-time graph gives the change in velocity over that time interval.
18. A train starts from rest and attains a velocity of $20 \, m/s$ in 10 seconds. Find its acceleration.
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Using $a = \frac{v - u}{t}$, with $u = 0$, $v = 20 \, m/s$, $t = 10 \, s$, we get $a = \frac{20 - 0}{10} = 2 \, m/s^2$.
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