Using MRUA formulas (Uniformly Accelerated Rectilinear Motion), find the speed that a body acquires that has an initial speed of 35 m/s and decelerates at a rate of 7 m/s^2 (that is, its speed decreases at a rate of 7 m/s for every second that passes). What is the time that passes for the body to come to a complete stop, that is, when its final speed is ZERO
The Correct Answer and Explanation is:
To solve this problem, we use the Uniformly Accelerated Rectilinear Motion (MRUA) formulas. The situation describes a body decelerating (slowing down) from an initial speed of 35 m/s at a constant rate of 7 m/s² until it comes to a complete stop (final speed is 0 m/s).
1. Given:
- Initial speed v0=35 m/sv_0 = 35 \, \text{m/s}v0=35m/s
- Final speed v=0 m/sv = 0 \, \text{m/s}v=0m/s
- Acceleration a=−7 m/s2a = -7 \, \text{m/s}^2a=−7m/s2 (negative because it is deceleration)
2. Formula to Use:
We use the MRUA formula: v=v0+atv = v_0 + a tv=v0+at
We need to find the time ttt when the final speed v=0v = 0v=0.
Substitute the known values: 0=35+(−7)t0 = 35 + (-7)t0=35+(−7)t 0=35−7t0 = 35 – 7t0=35−7t 7t=357t = 357t=35 t=357=5 secondst = \frac{35}{7} = 5 \, \text{seconds}t=735=5seconds
Answer:
- The body takes 5 seconds to come to a complete stop.
- At that point, its final speed is 0 m/s (as given).
Explanation:
In physics, uniformly accelerated rectilinear motion (MRUA) describes motion in a straight line where the acceleration is constant. When a body decelerates, it experiences a negative acceleration. This means that with every second that passes, the speed of the object decreases by a fixed amount.
In this problem, the body starts with an initial speed of 35 meters per second and decelerates at a rate of 7 meters per second squared. Since deceleration means the speed reduces steadily, the object’s speed reduces by 7 m/s every second.
To find how long it takes for the object to come to a complete stop (where the final speed is 0), we use the MRUA formula: v=v0+atv = v_0 + a tv=v0+at
Where:
- vvv is the final velocity,
- v0v_0v0 is the initial velocity,
- aaa is the acceleration,
- ttt is the time.
Plugging in the values: 0=35−7t0 = 35 – 7t0=35−7t. Solving this, we find that t=5t = 5t=5 seconds. This tells us that the body will continue to slow down for 5 seconds before it fully stops.
This makes sense because, with a deceleration of 7 m/s², each second reduces the speed by 7 m/s. In five seconds, the speed reduces by 5×7=35 m/s5 \times 7 = 35 \, \text{m/s}5×7=35m/s, which exactly cancels out the initial speed of 35 m/s, leaving the object at rest.
This analysis is a practical example of MRUA, demonstrating how time and acceleration relate to changes in velocity.
