Respuesta :
Answer:
4) Both objects undergo the same change in speed.
Explanation:
To find the change in speed in a time of 2s, we compare the rate of speed (difference of speed between 0 and 2s per unit time).
Given:
- acceleration =[tex]v_1(2)=v_1(0)+at[/tex] g = -9.8 m/s² (downward direction)
- 1st object's initial velocity (v₁(0)) = -5 m/s
- 2nd object's initial velocity (v₂(0)) = 10 m/s
Linear Motion with Constant Acceleration:
[tex]\boxed{velocity\ (v)=initial\ velocity\ (v_o)+acceleration\ (a)\times time(t)}[/tex]
[tex]\boxed{rate\ of\ velocity\ (a)=\frac{final\ velocity\ (v)-initial\ velocity\ (v_o)}{time\ difference\ (\Delta t)} }[/tex]
The velocity of 1st object after 2 seconds:
[tex]v_1(2)=v_1(0)+at[/tex]
[tex]=-5+(-9.8)(2)[/tex]
[tex]=-24.6\ m/s[/tex]
The rate of change after 2 seconds:
[tex]\displaystyle a_1=\frac{v_1(2)-v_1(0)}{2}[/tex]
[tex]\displaystyle=\frac{-24.6-(-5)}{2}[/tex]
[tex]=-9.8\ m/s^2[/tex]
The velocity of 2nd object after 2 seconds:
[tex]v_2(2)=v_2(0)+at[/tex]
[tex]=10+(-9.8)(2)[/tex]
[tex]=-9.6\ m/s[/tex]
The rate of change after 2 seconds:
[tex]\displaystyle a_2=\frac{v_2(2)-v_2(0)}{2}[/tex]
[tex]\displaystyle=\frac{-9.6-10}{2}[/tex]
[tex]=-9.8\ m/s^2[/tex]
Since a₁ = a₂, therefore both objects undergo the same change in speed.
Final answer:
Using the acceleration due to gravity (9.8 m/s2), the change in speed after 2 seconds for the object thrown downward is 19.6 m/s, while for the object thrown upward is 29.6 m/s. Therefore, the correct answer is 2).
Explanation:
To determine which object undergoes a greater change in speed in a time of 2 seconds, we can use the concept of acceleration due to gravity. For both objects, the acceleration due to gravity (g) is 9.8 m/s2.
For the object thrown downward, the initial velocity (u) is -5 m/s (negative because it is in the opposite direction to the acceleration due to gravity). After 2 seconds, the final velocity (v) can be calculated using v = u + gt.
For the object thrown upward, the initial velocity is 10 m/s. After 1 second, the object would have slowed down by 9.8 m/s, resulting in a velocity of 0.2 m/s upward.
After another second, the object would be traveling downward, resulting in a velocity change of 9.8 m/s for the second second. Hence, the total change in speed over 2 seconds is 10 m/s (initial) + 9.8 m/s + 9.8 m/s (from the two seconds of acceleration).
Now, calculating the change in speed for each object:
Object 1 (downward): v = -5 m/s + (9.8 m/s2 imes 2 s) = 14.6 m/s. Change in speed = final velocity - initial velocity = 14.6 m/s - (-5 m/s) = 19.6 m/s.
Object 2 (upward): Total change in speed = 10 m/s (initial) + 9.8 m/s (first second) + 9.8 m/s (second second) = 29.6 m/s.
Therefore, the second object has a greater change in speed over the 2 second period.
