The problem asks for the magnitude of the displacement of a ball thrown vertically upward after a certain time.
Physics Displacement Calculation
We can use the kinematic equation for displacement under constant acceleration:
\( \Delta y = v_0 t + \frac{1}{2} a t^2 \)
Where:
- \( \Delta y \) is the displacement.
- \( v_0 \) is the initial velocity.
- \( t \) is the time.
- \( a \) is the acceleration.
Applying Values to the Formula
Given:
- Initial velocity, \( v_0 = +30 \text{ m/s} \) (taking upward as positive).
- Time, \( t = 4 \text{ s} \).
- Acceleration due to gravity, \( a = -g = -10 \text{ m/s}^2 \) (acting downward).
Substitute these values into the equation:
\( \Delta y = (30 \text{ m/s})(4 \text{ s}) + \frac{1}{2} (-10 \text{ m/s}^2)(4 \text{ s})^2 \)
Step-by-Step Calculation
- Calculate the first term: \( v_0 t = 30 \times 4 = 120 \text{ m} \).
- Calculate the second term: \( \frac{1}{2} a t^2 = \frac{1}{2} (-10) (4)^2 = \frac{1}{2} (-10) (16) = -5 \times 16 = -80 \text{ m} \).
- Add the terms: \( \Delta y = 120 \text{ m} + (-80 \text{ m}) = 120 \text{ m} - 80 \text{ m} = 40 \text{ m} \).
The magnitude of the displacement after 4 seconds is 40 meters.
Similar Questions
- A ball thrown up vertically returns to the ground after 10 second. Find the velocity with which it was thrown up? (if g = 10 m/s2).
- A body falling from rest has a velocity '\(v\)' after it falls through a distance '\(h\)'. The distance it has to fall down further, for its velocity to become double, is _____ times '\(h\)' .
- By applying the brakes without causing a skid, the driver of a car is able to stop his car within a distance of 5 m, if it is going at 36 kmph. If the car were going at 72 kmph, using the same brakes, he can stop the car over a distance of:
- A ball, initially at rest, falls freely from the top of a building and reaches a maximum velocity of \(40\text{ m/s}\). Find the height of the building. (Use acceleration due to gravity, \(g = 10\text{ m/s}^2\))
- A car, starting from rest, is moving with a constant acceleration \(3\text{ m/s}^2\). Find the distance travelled by this car in \(10\text{ s}\).
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- A ball is thrown vertically upward with a speed of 30 m/s. The magnitude of its displacement after 4 s will be _____ (Take \(g = 10\ m/s^2\).)
A particle experiences constant acceleration for 20 s after starting from rest. If it travels a distance X 1, in the first 10 s and distance X 2in the remaining 10 s, then which of the following is true?
Important Questions from Kinematic equations for uniformly accelerated motion
Which of the following is an equation of motion?
I. u = v + at
II. 2as = v 2– u 2
- A ball is thrown vertically upward with a speed of 40 m/s. The time taken by the ball to reach the maximum height would be approximately
- A ball thrown up vertically returns to the ground after 10 second. Find the velocity with which it was thrown up? (if g = 10 m/s2).
Which of the following is an equation of motion?
I. u = v + at
II. 2as = v 2– u 2
A stone is dropped from a ballon going up with a uniform velocity of 5m/sec. If the ballon was 50 m high, then the stone was dropped, the height the ballon from ground when stone hits the ground will be:
(g = 10 m/s 2)
